2, 6, 12, 20, 30, 42, 56, (…..)
Perimeter of semi circular = πr+2r
Where r is radius , π = 22/7
πr+2r= 144 (given)
(22/7)r +2r = 144
22r+14r = 144*7 (multiply both sides by 7)
36r = 144*7
r= 144*7/36 = 28
radius =28 cm
Area =( 1/2)πr^2
Area=( 1/2 )*(22/7)*28*28
= 1232cm^2
Ans : area is 1232 cm^2
The formula to find number of diagonals (D) given total number of vertices or sides (N) is
N * (N – 3)
D = ———–
2
Using the formula, we get
1325 * 2 = N * (N – 3)
N2 – 3N – 2650 = 0
Solving the quadratic equation, we get N = 53 or -50
It is obvious that answer is 53 as number of vertices can not be negative.
Alternatively, you can derive the formula as triange has 0 diagonals, quadrangel has 2, pentagon has 5, hexagon has 9 and so on……
Hence the series is 0, 0, 0, 2, 5, 9, 14, …….. (as diagram with 1,2 or 3 vertices will have 0 diagonals).
Using the series one can arrive to the formula given above.
suppose
pipe:
A -30 hours A’s effeciency (60/30) =2
60( lcm of 30 and 20)
B- 20 hours B’s effeciency (60/20)=3
time taken by both to fill = 60/5 =12 as given in question (effeciencies of both a+b =2+3=5)
time taken by faster pipe i.e b = 60/3 =20
24*4= x(x+4)
solve this
answer is x=8
X+4= 12
77
X+x+2+x+3=42
3x+6=42
3x=42-6=36
X=12
X+2=14
X+3=15
Middle number 14
x-28=(1/3)x
x= 42
50 %of 42 = 21
325
3, 7, 15, 39, 63, 127, 255, 511
C. 39
3*2+1 = 7
15*2+1 = *31*
31*2+1 = 63
63*2+1 = 127
127*2+1 = 255
255*2+1 = 511
LET ACTUAL PRICE BE 100 RS(FOR CONVINIENCE)
THEREFORE IF PRICE IS CUT BY 20%
THEREFORE NEW PRICE=100-20=80 RS
THEREFORE WE NEED TO ADD X% TO 80 RS TO MAKE IT 20 RS AND ADD IT TO 80 TO MAKE IT 100RS
THEREFORE, 80X/100 = 20
I.E. 4X/5=20
THEREFORE x=20*5/4
=5*5
=25
HENCE 25% OF PRICE SHOULD BE ADDED TO MAKE THE PRICE EQUAL TO THE ACTUAL PRICE.
(x+2)+(x)+(x-2)
X+2+x+x-2=18
3x=18
X=6
The 3digit number is 864
Difference between 2 and 6 is = 4
Difference between 6 and 12 is = 6
Difference between 12 and 20 is = 8
Difference between 20 and 30 is = 10
Difference between 30 and 42 is = 12
Difference between 42 and 56 is = 14
So ne number will be with 16 Difference i .e 72
Therefore Answer will be 72